Find the volume of the solid obtained by rotating the region bounded by the curves: $y=x^8$ and $y=1$ about the line $y=6$.
I tried to use the washer method but then I cannot find two volumes that I can subtract one from the other to obtain the region. I also have tried the shell method by simply rotating the axes and making y the horizontal axis and x the vertical. I said that the volume of each shell in this case would be: $2\pi(6-y)(y^{1/8})dy\;$ but when I do the integration from $0$ to $1$ it doesn't give the right answer. Thank you.